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The discovery of the neutrino non-standard properties (mass and mixing) refocused on various aspects of the neutrino standard properties, both from the theoretical and the experimental side. In particular, precise measurements and modeling of the \(\nu \)-Nucleus Cross-Section in the intermediate energy range (\(\sim 0.5\)–5 GeV), and related Nuclear Effects, are now considered as fundamental issues. In fact, these become necessary for a more robust control of the systematic uncertainties relevant in the forthcoming experimental effort aiming at precision measurements of the MNSP matrix elements. A critical review of the present knowledge motivated the origin and the activity of a wide community progressively formed around these issues. In this introductory review we provide with a qualitative summary of the achievements from the current activity in this field.

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The Random Phase Approximation theory is used to calculate the total cross sections of electron neutrinos on \(^{12}\)C nucleus. The role of the excitation of the discrete spectrum is discussed. A comparison with electron scattering and muon capture data is presented. The cross section of electron neutrinos coming from muon decay at rest is calculated.

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I discuss the theoretical treatment of the electroweak nuclear response based on nonrelativistic nuclear many-body theory. This approach allows for a unified parameter-free description of a variety of kinematical regions relevant to many neutrino experiments. Selected applications to electron- and neutrino–nucleus scattering in the impulse approximation regime are analyzed.

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I will discuss the results of recent phenomenological study of unpolarized nuclear structure functions for a wide range of nuclei. As a basis of our phenomenology we develop a model which addresses a number of different mechanisms of nuclear scattering including corrections due to Fermi motion, binding, off-shell modification of the bound nucleon structure functions, nuclear shadowing, nuclear pion excess. The application of this approach to charged-current neutrino-nuclear scattering is also reviewed.

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The ICARUS and future liquid argon neutrino experiments generate demand for evaluating the spectral function of argon. In this paper we use oxygen nucleus as a testing ground for our phenomenological approach to the spectral function and probe the influence of momentum distribution and treatment of the mean field spectral function on the differential cross sections. The obtained model reproduces very well results of the exact spectral function of oxygen and can be applied to heavier nuclei, such as calcium or argon.

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We consider different methods and observables which can be obtained by the measurement of neutrino scattering off nucleons and nuclei with the purpose of finding evidence for the strange form factors of the nucleon, which enter into structure of the nucleonic weak neutral current.

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A relativistic distorted-wave impulse-approximation model is applied to quasi-elastic neutrino–nucleus scattering. Neutral-current and charge-current cross sections are evaluated. The strange quark contribution to nucleon form factors is calculated in view of the possibility of its determination. Particular attention is paid to the effect of final state interactions. Their influence on the determination of the strange form factors is investigated.

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Nuclear model effects in neutrino–nucleus quasielastic scattering are studied within the distorted wave impulse approximation, using a relativistic shell model to describe the nucleus, and comparing it with the relativistic Fermi gas. Both charged-current and neutral-current processes are considered and, for the neutral-current case, the uncertainties that nuclear effects may introduce in measurements of the axial strange form-factor of the nucleon are investigated.

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By means of a Monte Carlo cascade method, to account for the rescattering of the outgoing nucleon, we study the charged and neutral current inclusive one nucleon knockout reactions off nuclei induced by neutrinos. The nucleon emission process studied here is a clear signal for neutral-current neutrino driven reactions, and can be used in the analysis of future neutrino experiments.

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We compare local Fermi gas and shell model in muon capture in nuclei in order to estimate the effect of finite nuclear size in low energy weak reactions.

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We present general formulas for the production of the spin-3/2 and 1/2 resonances by neutrinos and then specialize to the first four resonances \(P_{33}(1232)\), \(P_{11}(1440)\), \(D_{13}(1520)\) and \(S_{11}(1535)\). The production of the resonances is described by vector and axial form-factors. We show how some of them could be determined from the electroproduction data and from the theory. Then we calculate the cross section for neutrino reactions and compare the results with the experimental data.

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An analysis of the Rein–Sehgal model in the context of the quark–hadron duality hypothesis is presented. The resonance region structure functions reconstructed from the Rein–Sehgal model at different values of \(Q^2_{\rm RES}\) are compared with the DIS structure functions calculated at higher \(Q^2_{\rm DIS}\). The ratios of corresponding integrals in the Nachtman variable are also calculated and presented as functions of \(Q^{2}_{\rm RES}\). The obtained functions are approximately flat for \(Q^2_{\rm RES}\gt 0.5\) GeV\(^2\) but the quark–hadron duality is not observed.

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The positivity constraints for hadronic tensor lead to the bounds for \(\tau \) lepton polarization in Parity Violating DIS. Another model-independent constraints are provided by the QCD duality which may be described in a similar way to QCD sum rules method. The Parity Conserving spin-dependent case is considered in more detail, while several specific comments on Parity Violating case are made. The observation is made that \({\mit \Delta }(1232)\) resonance should be excluded from duality consideration and possible reason for that is offered.

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We analyse available experimental data on the total charged-current \({\nu }N\) and \(\overline {\nu }N\) cross sections for quasielastic scattering and single-pion neutrinoproduction. Published results from the relevant experiments at ANL, BNL, FNAL, CERN, and IHEP are included dating from the end of sixties to the present day, covering \(\nu _{\mu }\) and \(\overline {\nu }_{\mu }\) beams on a variety of nuclear targets, with energies from the thresholds to about \(350\) GeV. The data are used to adjust the poorly known values of the axial masses.

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A Universal Object-Oriented/C++ Neutrino Monte Carlo Generator (GENIE) is briefly described. The purpose of this large scale software system is to become the “canonical” Monte Carlo for Neutrino Interaction Physics whose validity will extend to all neutrino types and nuclear targets in the energy range from a few MeV to hundreds of TeV. GENIE attempts to unify the Monte Carlo generation approaches used by a host of different, smaller procedural systems in a modern object-oriented software design. It is already a mature software system that currently consists of \(\sim 100\,000\) lines of C++ code (\(\sim 350\) classes organised in \(\sim 40\) packages). The first official, extensively validated, release of the GENIE Monte Carlo (version 2.0.0) is now publicly available. This production version is primarily intended for the on-going analyses of the MINOS experiment, since it features a complete adaptation of NeuGEN [H. Gallagher, Nucl. Phys. Proc. Suppl. 112, 188 (2002)], its presently used legacy Monte Carlo generator.

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FLUKA is a general purpose Monte Carlo code for transport and interaction of particles. In particular it contains detailed nuclear models which have been successfully tested in hadronic interactions. The same approach can be successfully applied to neutrino interactions. Here we review the main features of the FLUKA nuclear models and their application to the generations of interactions of neutrinos with E\(\ge \)100 MeV and proton decay.

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Results from the Wrocław Monte Carlo neutrino generator of events are reported. Predictions for charged hadron multiplicities, neutral pion and strange particle production are presented and compared with available data.

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The poor precision of neutrino–nucleus scattering data has become a driving component of the systematic error budgets of new long-baseline oscillation experiments. By building an active detector designed to make use of the high-intensity neutrino beams developed for oscillation experiments, higher precision studies of neutrino scattering processes can be undertaken. MINER\(\nu \)A, a compact, fully-active detector has been proposed to employ the NuMI beam at Fermilab, and will be able to dramatically improve the statistical precision of measured scattering cross-sections. It will also be instrumented to study, in detail, the effects of the nuclear medium on neutrino physics processes.

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A 2 km LAr detector would be an important asset for the T2K experiment. Different physics scenarios are considered and for each one the role of a LAr TPC in enhancing the ultimate sensitivity on \(\theta _{13}\) is studied. The large sample of neutrino interactions in the GeV region would provide crucial information for the study of different types of reactions and of nuclear effects, whereas the inner target would give a direct measurement of the cross sections ratio between Water and Argon. Such a detector would also be an important milestone for the LAr TPC technique providing an extremely valuable experience for future large LAr detectors.

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This article presents methods of distinguishing \(\nu _\mu \) NC \(\pi ^0\) production from \(\nu _e\) CC electron production events in liquid argon TPC detector. This is important in estimation of the intrinsic \(\nu _e\) component in the beam in long-baseline neutrino experiments. One of the methods — based on finding a gap between primary vertex of interaction and the beginning of electromagnetic shower — is evaluated for T2K experimental setup with liquid argon TPC in 2 km station of the experiment.

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Neutrino propagation in protoneutron stars requires the knowledge of the composition as well as the dynamical response function of dense hadronic matter. Matter at very high densities is probably composed of other particles than nucleons and little is known on the Fermi liquid properties of hadronic multicomponent systems. We will discuss the effects that the presence of \({\mit \Lambda }\) hyperons might have on the response and, in particular, on its influence on the thermodynamical stability of the system and the mean free path of neutrinos in dense matter.

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Neutrinos from astrophysical sources carry unique information, complementary to the photons, that is of extraordinarily value to develop our understanding of these objects. Two sources: the Sun and Supernova 1987A have already been observed in neutrinos, and future experiments are expected to detect \(\nu \) in different energy ranges from several other sources. This includes \(E_\nu \sim 10\) MeV \(\nu \) from gravitational collapse Supernovae and very high energy \(\nu \) (\(E_\nu \gtrsim 1\) TeV) from sources like young supernova Remnants, Gamma Ray Bursts or Active Galactic Nuclei that are likely acceleration sites for cosmic rays. Other more exotic sources are also possible, of particular interest is the search of \(\nu \) from Dark Matter annihilation in the center of the Earth and the Sun. The \(\nu \) observations have the potential to deeply enrich our vision and understanding of the Universe around us.